It would have behooved John Tortorella well before the Rangers canned him to ask for a sit-down with Tom Coughlin, a request Coughlin no-doubt would have granted, a meeting that might have saved Tortorella’s hide.

Coughlin was once — well, a whole lot more than once — abrasive to those around him in the work environment, certainly too petty with the media and, more importantly, uncaring about the ever-widening disconnect he fostered with his players.

Coughlin was in real trouble, job security-wise, until he listened to family and confidants around him and heeded co-owner John Mara’s decidedly unsubtle suggestion to change his often boorish ways.

The results — two Super Bowl triumphs later — is a still-stern head coach who masterfully eradicated player distrust, a failing that apparently doomed Tortorella. Coughlin even at age 66, now more fully understands how to navigate a locker room filled with athletes young enough to be his grandsons. The dynamic from season to season can change, though, and Coughlin with this particular Giants team has an interesting motivational hammer he is able to wield.

“With a lot of one-years [contracts] out there, guys looking for something more long-term, it definitely creates more of a sense or hunger by going out there with something to prove,’’ safety Stevie Brown said.

Brown is one of the “one years’’ who will make up nearly half of the Giants’ regular-season roster. As a restricted free agent, Brown is playing on a one-year tender of $2 million after coming seemingly out of nowhere to lead the team with eight interceptions, admirably filling in for oft-injured Kenny Phillips.

“I’m still thankful for the tender I got,” Brown said. “I’ll never downplay it, but at the same time you always want something that’s long-term, you want to have something with a little more insurance.

“It’s another ‘show-me’ with a little more money is all it is.’’

Yup, it’s a “show-me’’ year ahead for so many Giants. The only free agent deemed worthy of a multi-year deal was defensive tackle Cullen Jenkins. The others were fortunate to get one-year, mostly minimum-salary contracts. The Giants provided their own free agents — guard Kevin Boothe, and linebacker Keith Rivers — with the same low-security offers. Many other holdovers, notably receiver Hakeem Nicks, defensive end Justin Tuck and cornerback Corey Webster, are entering the final year of their contracts. As many as 24 players on the final roster will have no financial security after the 2013 season.

One-year deals have taken over the NFL, with big money reserved for a select few, which is why Boothe surveyed the open market and estimated “everybody’s disappointed except for five people.’’

In the world of non-guaranteed contracts, living on the edge is a way of NFL life, but operating on a one-year deal is the riskiest existence.